I am trying to figure out the numbers, but it sounds worrisome to me; could be just my past experience speaking though and each persons is unique. What is the rated tow capacity for the truck, the gCwr for the truck? If gCwr is exceeded, even if payload and hitch-weight are not exceeded, you could be looking at issues. Also, gas engines have reach peak torque/towing power, at much higher rpms, harder on engine, than diesel engines (roughly 3,800 rpm v. 1,400 rpm) which affects how hard the engine has to work.
I had a similar thought process in the past, concentrating on payload and tongue weights with less attention to gcwr because I thought the engine was great and could exceed limits because of some modifications I made. I drove easily across plains/prairies and even the east coast--but come the Laurentians or Rockies, the engine pulled it like I though, but I went through three transmissions.
I would, in addition to what you have checked, check tow capacity of truck (online chart) and gCwr, go to scale and weigh truck as though loaded, mentally add the GVWR of the trailer...not the dry weight but the max gross vehicle weight rating (because you WILL be adding your personal effects to the trailer, and generally people max out their gvwr, loaded weight). Truck loaded weight + trailer loaded weight should not exceed gcwr of truck or gvwr of trailer, else you increase likelihood of blowouts or transmission problems and significantly increase effort of engine, which tends to play out in hilly or mountainous terrain. If you have done that, you are not likely to face issues, beyond the age and mileage of the truck.
I used to pull a Keystone Cougar with a dry weight of 6,700 lbs, but a gvwr of 9,500 lbs, with a 2018 Ram 1500 Express, tow capacity 10,500 lbs. Sounded like it should work, but even getting close to limits can cause issues. Going over the Coquihalla, (aka: highway through hell), I noticed my new truck was struggling, had to drop speed significantly, and it was almost banging into gears. Clearly, issues would arise in the future. When subsequently driving it without the trailer attached, I could feel the engine still trying to surge and low gears sort of clunked as they changed. Got rid of truck and bought an F350 6/7L Lariat with almost triple the tow capacity--can't even tell I am pulling a trailer now and getting similar fuel consumption. Maxing out towing capacity just seems like asking for trouble to me. When I get travel trailers, I like to keep them, loaded, several thousand lbs below gcwr of truck.